Hopf Algebras, Their Actions on Rings, and Graded Algebras

Hopf 代数、它们对环的作用以及分级代数

• 批准号: 9802086
• 负责人: Susan Montgomery
• 金额: $ 13.09万
• 依托单位: University of Southern California
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-07-01 至 2002-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9802086&HistoricalAwards=false
• 关键词: Hopf; Algebras; Their; Actions; Rings

9802086 Montgomery This award supports work on Hopf algebras and related structures. The principal investigator will compare the prime ideals of a Hopf crossed product with the prime ideals of the underlying algebra on which the Hopf algebra acts. More generally, she will compare the primes in a Hopf Galois extension. She will also study "duality problems" involving both the action of a Hopf algebra and of a suitable dual Hopf algebra, in order to look at the prime ideals for infinite dimensional Hopf algebras. Problems on classifying finite-dimensional Hopf algebras will also be considered in the context of Yetter-Drinfeld categories. Finally some problems concerning algebras graded by groups will be considered. This research is concerned with an algebraic object called a Hopf algebra. While the area is quite technical, Hopf algebras are becoming of increasing interest, even to nonmathematicians. Hopf algebras are useful for studying the type of knot theory that appears in molecular chemistry. Certain types of Hopf algebras are now referred to as quantum groups in recognition of the applications in physics. Hopf algebras are used to study differential operators and to make combinatorics more like calculus.

9802086蒙哥马利该奖项支持HOPF代数及相关结构的工作。 首席研究者将将跨越产品的主要理想与霍普夫代数行动的基本代数的主要理想进行比较。 更普遍地，她将比较霍普夫·加洛伊斯（Hopf Galois）扩展中的素数。 她还将研究涉及Hopf代数和合适双Hopf代数的作用的“二元性问题”，以研究无限尺寸HOPF代数的主要理想。 在Yetter-Drinfeld类别的背景下，也将考虑对有限维HOPF代数进行分类的问题。 最后，将考虑有关按组对代数分级的一些问题。 这项研究与称为HOPF代数的代数对象有关。 尽管该领域非常技术性，但HOPF代数也变得越来越兴趣，即使是非音乐家。 HOPF代数可用于研究分子化学中出现的结理论类型。 现在，某些类型的HOPF代数被称为量子组，以识别物理中的应用。 HOPF代数用于研究差异操作员，并使组合学更像微积分。